Hmmm... sounds as though you are describing
"..bugs that need to be fixed by changing the code."

Just an (unattributed) quote.   ;-)

Andrew T.

What data if it's affected by the null reference?

I could see getting into a lot of trouble trying to save data
gracefully after a NPE.

I have developed an app along these lines. There's a FooThread class and
a FooThreadFactory, constructors and other methods, and stuff like:

public void run () {
    try {
        some stuff
    } catch (RuntimeException e) {
        factory.notifyThreadDeath(this, e);
        throw e;
    } catch (OutOfMemoryError e) {
        app.saveStuff();
        factory.shutDown();
        factory.notifyThreadDeath(this, e);
        throw e;
    } catch (Error e) {
        factory.notifyThreadDeath(this, e);
        throw e;
    }
}

Unexpected exceptions are caught and rethrown. Anything other than OOME
results in the thread factory being notified via a
notifyThreadDeath(FooThread, Throwable) method. This logs the stack
trace and decrements a thread count. Elsewhere the factory has a
periodically-called method to interrupt or start threads as need be,
based on a desired number (depending on the number of requests
occurring) and the actual number. (It also keeps a collection of the
actual thread objects, so it can pick some at random to interrupt. The
stuff in the try block involves taking a request off a blocking queue
and handling it in an endless while loop. There's a try that catches
InterruptedExceptions and breaks the while loop, also calling
factory.notifyThreadDeath(this, null).

Upshot: stack traces are logged so things can be debugged. Request
servicing continues, and doesn't even diminish in capacity since the
thread that dies is recreated immediately unless it's no longer needed
anyway. The code that loops the factory's thread-management method
periodically just does so and sleeps, and doesn't do anything that's at
all exception prone itself (it doesn't new anything, for instance,
except thread objects when necessary). OOME causes it to save some data
(mostly caches) and shut down gracefully. (I note that even though the
total megabytage of live objects should remain bounded, it does
eventually slow down and then catch OOME if it runs a long time. Heap
fragmentation?) Restarting the process if it dies somehow is handled
externally. Since it's a network using app, most exceptions are I/O
exceptions that get handled closer to the source, usually by sending the
client an error message and moving on to the next request; they tend to
indicate a problem with connectivity or the client having sent a bad or
malformed request that includes a bogus URL, parse error, or similarly.
Still, the odd wackiness trickles up from time to time. I've had library
code randomly bubble up NPEs and various IndexOutOfBoundsException
flavours, for example, on rare occasions. Lately (since the deployment
environment switched to the Java 6 beta runtime environment) there've
been NPEs coming out of Sun code we can't explain (mainly from one
particular PriorityQueue deep in the bowels of the app -- I found an "in
progress, bug" bug on Sun's site about this one, where someone had it
occur with a comparator not consistent with the objects' equals method,
which is the case in my code also. A quick check of this newsgroup turns
up a complaint of something similar again.) The app recovers from all of
these insults with maybe one in ten thousand requests ending up
incompletely processed. The transaction gets rolled back, but
transactions are pretty much independent of each other, and client
requests that are well-formed but get a "temporary service error"
message are resubmitted by the client after a backoff delay anyway.

A noble cause indeed.  You may also wish to open a JDialog (assuming a
GUI application) which alerts to the user that a problem occured. Just
don't give them too much detail unless they ask for it though.

setDefaultUncaughtExceptionHandler is definetly the way to go in order
to detect uncaught exceptions.  It will catch almost all
RuntimeExceptions and Errors.  I have had issues catching
OutOfMemoryException, but the JVM is often a in a pretty big fubar
state by that time.